The figure shown is a speed-time graph for a body moving in a straight line. Given that its initial speed was five meters per second, determine the body’s acceleration during the part of the journey where the body was accelerating.
There are three parts to the figure here. The first part, the slope is going upwards. This means that the body is accelerating. In the second part, where it is horizontal, the body is travelling at a constant speed. And in the third part, where the slope is going downwards from left to right, it is decelerating or slowing down. In this question, we are interested in the first part of the journey. We will solve this problem using one of the equations of motion, 𝑣 equals 𝑢 plus 𝑎𝑡, where the 𝑢 is our initial velocity. 𝑣 is our final velocity. 𝑎 is the acceleration and 𝑡 is the time.
Using the figure shown, we can see that the initial velocity is five meters per second. The final velocity, in the first part of the journey, is 45 meters per second. The time taken for this journey was five seconds. And the acceleration is unknown. Substituting these values into the equation, 𝑣 equals 𝑢 plus 𝑎𝑡 gives us 45 equals five plus five 𝑎. Subtracting five from both sides of this equation, gives us 40 equals five 𝑎. And finally, dividing both sides by five gives us 𝑎 is equal to eight.
This means that the acceleration during the part of the journey where the body was accelerating, was eight meters per second squared. We could also have calculated this acceleration directly from the figure or graph. The acceleration on a speed-time graph is the same as the gradient. And in this case, the gradient of the first part of the graph was eight.