Kinematics Big Review

The graph above shows the velocity versus time for an object moving in a straight line. At what time after t = 0 does the object again pass through its initial position?

• 1 s

• Between 1 and 2 s

• 2 s

• Between 2 and 3 s

Answer explanation

Area bounded by the curve is the displacement By inspection the negative area between 0 and 1s

will be countered by an equal negative area sometime between 1 and 2s.

A diver initially moving horizontally with speed v dives off the edge of a vertical cliff and lands in the water a distance d from the base of the cliff. How far from the base of the cliff would the diver have landed if the diver initially had been moving horizontally with speed 2v?

• d 

• 2d 

• 4d

Answer explanation

The time in the air for a horizontal projectile is dependent on the height and independent of the

initial speed. Since the time in the air is the same at speed v and at speed 2v, the distance (d = vt)

will be twice as much at a speed of 2v

A ball is thrown and follows the parabolic path shown above. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground. How do the speeds of the ball at the three points compare?

• v_P < v_Q < v_R

• v_R < v_Q < v_P

• v_Q < v_R < v_P

• v_Q< v_P = v_R

Answer explanation

At the top of its path, the vertical component of the velocity is zero, which makes the speed at the

top a minimum. With symmetry, the projectile has the same speed when at the same height,

whether moving up or down.

A ball is thrown and follows the parabolic path shown above. Air friction is negligible. Point Q is the highest point on the path. Points P and R are the same height above the ground. Which of the following diagrams best shows the direction of the acceleration of the ball at point P?

• 
• 

Answer explanation

g points down in projectile motion. Always.

The graph above represents position x versus time t for an object being acted on by a constant force. The average speed during the interval between 1 s and 2 s is most nearly

(A)     (B)    (C)     (D)

• 2 m/s 

• 4 m/s  

• 5 m/s 

• 6 m/s

Answer explanation

Average speed = total distance/total time = (8 m – 2 m)/(1 second)

At time t = 0, car X traveling with speed v₀ passes car Y which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus time t for both cars are shown above. Which of the following is true at time t = 20 seconds?

• Car Y is behind car X. 

• Car Y is passing car X.

• Car Y is in front of car X.

• Car X is accelerating faster than car Y.

Answer explanation

The area under the curve is the displacement. There is more area under the curve for Car X.

At time t = 0, car X traveling with speed v₀ passes car Y which is just starting to move. Both cars then travel on two parallel lanes of the same straight road. The graphs of speed v versus time t for both cars are shown above. 1.      From time t = 0 to time t = 40 seconds, the areas under both curves are equal. Therefore, which of the following is true at time t = 40 seconds?

• Car Y is behind car X. 

• Car Y is passing car X.

• Car Y is in front of car X.

• Car X is accelerating faster than car Y.

Answer explanation

Area under the curve is the displacement. Car Y is moving faster as they reach the same point.

The graph above shows the velocity v as a function of time t for an object moving in a straight line. Which of the following graphs shows the corresponding displacement x as a function of time t for the same time interval?

• 
• 
• 
• 

Answer explanation

A velocity-time graph represents the slope of the displacement-time graph. Analyzing the v-t

graph shows an increasing slope, then a constant slope, then a decreasing slope (to zero)

A target T lies flat on the ground 3 m from the side of a building that is 10 m tall, as shown above. A student rolls a ball off the horizontal roof of the building in the direction of the target. Air resistance is negligible. The horizontal speed with which the ball must leave the roof if it is to strike the target is most nearly

• 3/10 m/s

• 3 m/s

Answer explanation

For a horizontal projectile, the initial speed does not affect the time in the air. Use v0y = 0 with 10 m = ½ gt2 to get t = root 2 For the horizontal part of the motion; v = d/t

A student is testing the kinematic equations for uniformly accelerated motion by measuring the time it takes for light-weight plastic balls to fall to the floor from a height of 3 m in the lab. The student predicts the time to fall using g as 9.80 m/s² but finds the measured time to be 35% greater. Which of the following is the most likely cause of the large percent error?

• The acceleration due to gravity is 70% greater than 9.80 m/s² at this location.

• The acceleration due to gravity is 70% less than 9.80 m/s² at this location.

• Air resistance increases the downward acceleration.

• The acceleration of the plastic balls is not uniform.

Answer explanation

By process of elimination (A and B are unrealistic; C is wrong, air resistance should decrease the

acceleration)