Kinematics Practice Test 2

1.

A particle moves along the x-axis so that its position is given by \( x(t) = 4t^2 - 3t + 2 \) (in meters, t in seconds). What is the particle's acceleration at \( t = 2 \) s?

a) 8 m/s² b) 5 m/s² c) 4 m/s² d) 1 m/s²

2.

A projectile is launched from ground level with speed \( v_0 \) at angle \( \theta \) above the horizontal. What is the total time of flight?

a) \( \frac{v_0^2 \sin2\theta}{g} \) b) \( \frac{v_0 \sin\theta}{g} \) c) \( \frac{2v_0 \cos\theta}{g} \) d) \( \frac{2v_0 \sin\theta}{g} \)

3.

A car accelerates from rest with a time-dependent acceleration \( a(t) = 8t \) m/s². What is its velocity after 2 seconds?

a) 32 m/s b) 24 m/s c) 16 m/s d) 8 m/s

4.

A ball is thrown vertically upward with initial velocity \( v_0 \). At what height is its speed exactly half of what it will be just before hitting the ground?

a) \( \frac{3}{4}h_{max} \) b) \( \frac{1}{2}h_{max} \) c) \( \frac{1}{4}h_{max} \) d) \( \frac{2}{3}h_{max} \)

5.

A particle moves in the plane with velocity \( \vec{v}(t) = (2t)\hat{i} + (5)\hat{j} \) m/s. If it starts at the origin, what is its position vector at \( t = 3 \) s?

a) \( (6\hat{i} + 10\hat{j}) \) m b) \( (9\hat{i} + 15\hat{j}) \) m c) \( (3\hat{i} + 5\hat{j}) \) m d) \( (12\hat{i} + 15\hat{j}) \) m

6.

A train moves with constant acceleration. It passes point A with speed 12 m/s and point B, 180 m further, with speed 24 m/s. What is the acceleration?

a) 1.2 m/s² b) 2.4 m/s² c) 0.8 m/s² d) 1.6 m/s²

7.

A particle starts from rest and moves along a straight line with acceleration \( a(x) = 4x \) m/s². What is its speed when it has traveled 3 m?

a) 3.5 m/s b) 4.9 m/s c) 6.9 m/s d) 2.4 m/s

8.

A projectile is launched from height \( h \) above the ground with initial speed \( v_0 \) at angle \( \theta \). What is the horizontal range?

a)\( \frac{2v_0^2 \sin\theta \cos\theta}{g} \) b) \( \frac{v_0^2 \sin2\theta}{g} \) c) \( \frac{v_0 \cos\theta}{g} (v_0 \sin\theta + \sqrt{(v_0 \sin\theta)^2 + 2gh}) \) d) \( \frac{v_0 \sin\theta}{g} \)

9.

A particle moves so that its velocity is given by \( v(t) = Bt^2 + C \), where \( B \) and \( C \) are constants. If \( x = 0 \) at \( t = 0 \), what is its position at time \( t \)?

a) \( Bt^2 + Ct \) b) \( \frac{B}{2}t^2 + Ct \) c) \( Bt^3 + C \) d) \( \frac{B}{3}t^3 + Ct \)

10.

A boat heads due east across a river with speed 6 m/s relative to the water. The river flows north at 8 m/s. What is the magnitude of the boat's velocity relative to the ground?

a) 10.0 m/s b) 12.0 m/s c) 14.0 m/s d) 8.0 m/s

11.

A particle moves along the y-axis so that its velocity is given by \( v(t) = 3e^{0.4t} \) m/s. If \( y = 0 \) at \( t = 0 \), what is its position at \( t = 2 \) s?

a) 7.45 m b) 5.00 m c) 4.00 m d) 2.72 m

12.

A ball is dropped from a height \( h \) above the ground. At what height is its speed exactly half of what it will be just before hitting the ground?

a) \( \frac{3}{4}h \) b) \( \frac{1}{2}h \) c) \( \frac{1}{4}h \) d) \( \frac{2}{3}h \)

13.

A particle moves so that its acceleration is \( a(t) = 10t^2 \) m/s². If its initial velocity is zero, what is its displacement after 2 seconds?

a) 7.66 m b) 13.33 m c) 20.00 m d) 24.00 m

14.

A projectile is launched at speed \( v_0 \) from a cliff of height \( h \) above level ground at angle \( \theta \) above the horizontal. Which of the following best describes the time to reach the ground?

a) \( \frac{2v_0 \sin\theta}{g} \) b) The positive root of \( y(t) = h + v_0 \sin\theta\, t - \frac{1}{2}gt^2 = 0 \) c) \( \frac{v_0 \sin\theta}{g} \) d) \( \frac{v_0^2 \sin2\theta}{g} \)

15.

A particle moves along a straight line with velocity \( v(x) = 5x \) m/s, where \( x \) is in meters. If it starts from \( x = 2 \) m at \( t = 0 \), how long does it take to reach \( x = 6 \) m?

a) 0.28 s b) 0.40 s c) 0.69 s d) 0.80 s

16.

A car moves such that its velocity is \( v(t) = 15 - 3t \) m/s. At what time does it come to rest?

a) 5 s b) 10 s c) 2 s d) 20 s

17.

A particle moves in a circle of radius 3 m such that its tangential acceleration is constant at 4 m/s². If it starts from rest, what is its speed after completing one full revolution?

a) 12.2 m/s b) 6.9 m/s c) 4.9 m/s d) 8.7 m/s

18.

A particle moves along the x-axis with velocity \( v(t) = 3t^2 - 6t + 2 \) m/s. What is the particle's acceleration at \( t = 2 \) s?

a) 4 m/s² b) 8 m/s² c) 10 m/s² d) 6 m/s²

19.

A projectile is launched horizontally from a height \( h \) with speed \( v_0 \). How long does it take to reach the ground?

a) \( \sqrt{\frac{2h}{g}} \) b) \( \frac{h}{v_0} \) c) \( \frac{v_0}{g} \) d) \( \sqrt{\frac{h}{g}} \)

20.

A car travels 2 km at 30 m/s and then another 2 km at 60 m/s. What is its average speed for the entire trip?

a) 40.0 m/s b) 45.0 m/s c) 50.0 m/s d) 55.0 m/s

21.

A particle moves along the x-axis with position given by \( x(t) = 2t^3 - 9t^2 + 12t + 5 \) (in meters, t in seconds). At what time(s) is the particle at rest?

a) t = 1 s and t = 2 s b) t = 0 s and t = 3 s c) t = 1.5 s only d) t = 2 s only

22.

A car accelerates from rest at a constant rate of 3.0 m/s² for 8.0 seconds, then maintains a constant velocity for 12.0 seconds, and finally decelerates at 2.0 m/s² until it comes to rest. What is the total distance traveled by the car?

a) 528 m b) 384 m c) 432 m d) 576 m

23.

A particle moves in a straight line with acceleration \( a(t) = 6t - 4 \) m/s². If the particle starts from rest at t = 0, what is its velocity at t = 3 s?

a) 9 m/s b) 15 m/s c) 21 m/s d) 27 m/s

24.

A ball is thrown vertically upward with an initial velocity of 25 m/s. How long does it take for the ball to reach a height of 20 m above its starting point?

a) 1.0 s b) 1.5 s c) 2.0 s d) 2.5 s

25.

A particle moves along the x-axis with velocity \( v(t) = 4t^2 - 6t + 2 \) m/s. What is the average acceleration of the particle from t = 0 to t = 4 s?

a) 8 m/s² b) 10 m/s² c) 12 m/s² d) 14 m/s²

26.

A car traveling at 30 m/s applies its brakes and comes to rest in 6.0 seconds. Assuming constant deceleration, what is the stopping distance?

a) 90 m b) 120 m c) 150 m d) 180 m

27.

A particle moves with position function \( x(t) = t^3 - 6t^2 + 9t + 2 \). At what time(s) does the particle change direction?

a) t = 1 s and t = 3 s b) t = 2 s only c) t = 1.5 s only d) t = 0 s and t = 4 s

28.

A train accelerates from rest at 0.5 m/s² for 60 seconds, then travels at constant speed for 300 seconds, and finally decelerates at 0.3 m/s² until it stops. What is the total distance traveled?

a) 9,000 m b) 10,500 m c) 11,400 m d) 15,000 m

29.

A particle moves with acceleration \( a(t) = 2t + 1 \) m/s². If the particle has an initial velocity of 5 m/s and starts at x = 0, what is its position at t = 4 s?

a) 32 m b) 40 m c) 49 m d) 56 m

30.

A ball is dropped from a height of 80 m. At the same instant, another ball is thrown upward from the ground with an initial velocity of 40 m/s. When do the balls meet?

a) 1.0 s b) 1.5 s c) 2.0 s d) 2.5 s

Kinematics Practice Test 2

30 Questions – Mixed Conceptual & Calculations