Question

Two cars (Car A and Car B) travel in a straight line at an initial speed of 8.0 meters per second. Both cars eventually reach the same final velocity. CAR A accelerates uniformly at a rate of 1.5 meters per second squared, over a distance of 44 meters. It takes CAR B 75 meters to reach the same speed. What is the magnitude of the acceleration of CAR B?

A. 1.0 m/s^2
B. 1.2 m/s^2
C. 1.5 m/s^2
D. 1.8 m/s^2

Answer 1

To find Car B's acceleration, use the kinematic equation linking initial and final velocity, acceleration, and distance, then solve for acceleration using the information given for both cars.

Step-by-step explanation:

To determine the magnitude of the acceleration of Car B, the kinematic equation that relates initial velocity, final velocity, acceleration, and distance travelled can be used:

v2 = u2 + 2as

Where:

• v is the final velocity,
• u is the initial velocity,
• a is the acceleration,
• s is the distance travelled.
• Since both cars reach the same final velocity, we can set up the equation for Car A to solve for its final velocity, and then use that to find the acceleration for Car B.

For Car A: v2 = 82 + 2(1.5)(44)

Once we have the final velocity, we use it to calculate Car B's acceleration:

For Car B: v2 = 82 + 2a(75)

By rearranging the equation for Car B to solve for 'a', we would find the acceleration of Car B which would correspond to the answer choice closest to the calculated value.