Acceleration and Deceleration Problem

The Physics Problem: Calculating Time and Distance

Question:

A car starts from rest and accelerates in a straight line at 2 m/s² until it reaches a speed of 20 m/s. Then, it begins to slow down at a constant rate of 1 m/s² until it stops. We need to find:

1. The total time taken for the car to go from start to stop.
2. The total distance covered by the car from start to stop.

Solution: Breaking Down the Motion into Phases

To solve this problem, we will divide the motion of the car into two phases:

Phase 1 - Acceleration

• The car starts from rest (initial velocity v₀ = 0) and accelerates at 2 m/s².
• We determine the time taken to reach 20 m/s and the distance covered during this phase using the formula: x - x₀ = v₀t + (1/2)at².

Phase 2 - Deceleration

• After reaching 20 m/s, the car starts slowing down at 1 m/s².
• The time and distance for the car to stop from 20 m/s are calculated using the same kinematic formula.

By applying these principles and calculations for each phase, we can find the total time and distance for the car's journey from start to stop.