Question

A car starts moving at 85 m/s for 10 seconds. Then the car decelerates for 5 seconds to 30 m/s. After 10 more seconds, the car is traveling 120 m/s and continues at this speed for 10 additional seconds. What is the acceleration of the car between seconds 10 and 15?

a) -11 m/s²
b) -9 m/s²
c) -6 m/s²
d) -3 m/s²

Answer 1

The acceleration of the car between seconds 10 and 15, as it decelerates from 85 m/s to 30 m/s in 5 seconds, is calculated to be -11 m/s².

Step-by-step explanation:

The problem describes a car's velocity changing over time, and we are asked to calculate the acceleration of the car between seconds 10 and 15, which is when the car decelerates from 85 m/s to 30 m/s over 5 seconds. Acceleration is defined as the rate of change of velocity over time. The formula to calculate acceleration (a) is a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time.

To find the acceleration between seconds 10 and 15, we use the initial velocity (vi) of 85 m/s and the final velocity (vf) of 30 m/s. The change in velocity (Δv) is vf - vi = 30 m/s - 85 m/s = -55 m/s. The change in time (Δt) is 5 seconds. Thus, the acceleration is a = -55 m/s / 5 s = -11 m/s². This means the car's velocity decreases by 11 m/s each second during this time period, indicating a negative acceleration or deceleration.