Calculating Car's Acceleration in Two Different Phases of Motion

A car starts from rest and accelerates uniformly to 10 m/s in just 5 seconds. Find the car's acceleration.

Final answer:

The car's acceleration during the first 8 seconds is 1 m/s², and its deceleration during the last 6 seconds is -1 m/s².

Explanation:

Finding the Car's Acceleration

To find the car's acceleration during the two different phases of its motion, we use the formula for uniform acceleration: a = (v - u) / t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time taken to change the velocity.

First 8 Seconds

Initially, the car accelerates from 2 m/s to 10 m/s in 8 seconds. Using the formula:
a = (v - u) / t
a = (10 m/s - 2 m/s) / 8 s
a = 8 m/s / 8 s
a = 1 m/s²

The acceleration during the first 8 seconds is 1 m/s².

Last 6 Seconds

Then, it slows down to 4 m/s in the next 6 seconds. The acceleration (deceleration) will be negative:
a = (v - u) / t
a = (4 m/s - 10 m/s) / 6 s
a = -6 m/s / 6 s
a = -1 m/s²

The deceleration during the last 6 seconds is -1 m/s².