# Different Cases in Acceleration – Time Graph

## Different Cases in Acceleration – Time Graph

Acceleration is the rate at which the velocity changes with respect to time. It is measured in m/ sec² in standard unit system. To obtain acceleration vs. time graph we plot acceleration on y-axis and time on x-axis. There are three possible cases that we arrive on:

1. Particle is Moving with Constant Acceleration: Let at time t = 0, acceleration is a₀. Since acceleration is constant, so acceleration at any further time will remain a₀. Hence, acceleration – time graph for a particle moving with constant acceleration is a straight line parallel to time axis.

2. Particle is Moving with Increasing Acceleration at Constant Rate: Acceleration – Time graph for a particle moving with increasing acceleration at constant rate is a straight line making an acute angle α with time axis. Graph will be straight line because acceleration is increasing at constant rate.

3. Particle is Moving with Decreasing Acceleration at Constant Rate: Acceleration – Time graph for a particle moving with decreasing acceleration at constant rate is a straight line making an obtuse angle α with time axis. The graph will be a straight line because acceleration is decreasing at constant rate. Let at t = 0, acceleration is a₀. At sometime t = t₀, acceleration becomes zero and then it becomes negative.