Question

A monkey-mobile, driven by a monkey, is traveling at a velocity of 24.59 m/s when he sees a gorilla crossing in the middle of the road and slams on the brakes. It takes the car 4.2 seconds to come to rest, calculate the magnitude of the car's acceleration.

a) 2.6 m/s²
b) 5.8 m/s²
c) 11.67 m/s²
d) 9.14 m/s²

Answer 1

The magnitude of the car's acceleration is found by dividing the change in velocity by the time taken to stop. The correct answer, with a starting velocity of 24.59 m/s and a stopping time of 4.2 seconds, is 5.8 m/s².

Step-by-step explanation:

To calculate the magnitude of the car's acceleration, we can use the formula for acceleration:

a = (Δv) / t

where:

• Δv is the change in velocity (final velocity - initial velocity),
• t is the time taken to come to rest.

Here, the initial velocity (vi) is 24.59 m/s (since the car comes to rest, final velocity vf is 0 m/s), and the time (t) is 4.2 seconds.

Substituting the given values:

a = (0 m/s - 24.59 m/s) / 4.2 s
a = -24.59 m/s / 4.2 s
a = -5.85 m/s²

The negative sign indicates that the acceleration is in the opposite direction to the motion (deceleration). The magnitude of the acceleration is 5.85 m/s², so the correct answer is b) 5.8 m/s².