The velocity-time (v-t) graph for an object travelling in a straight line is shown below. Which of the following is the corresponding acceleration-time (a-t) graph?

The v-t graph shows two distinct phases:

• Phase 1: From $t=0$ to some time $t_1$ (where the graph crosses the t-axis), the velocity decreases linearly from a positive value to zero. This indicates a constant negative slope.
• Phase 2: From time $t_1$ onwards, the velocity continues to decrease linearly from zero to a negative value. This also indicates a constant negative slope.

Acceleration is the rate of change of velocity, which means it is the slope of the velocity-time graph.

• Since the v-t graph is a straight line with a constant negative slope throughout both phases, the acceleration must be constant and negative for the entire duration shown.

We are looking for an acceleration-time (a-t) graph that shows a constant negative acceleration.

• Graph A shows positive acceleration, then negative acceleration.
• Graph B shows negative acceleration, then positive acceleration.
• Graph C shows linearly increasing acceleration, then linearly decreasing acceleration.
• Graph D shows acceleration that decreases linearly, then increases linearly.
• Graph E shows a constant negative acceleration.

Based on our analysis, Graph E correctly represents a constant negative acceleration.

The final answer is $E$