A sprinter starts from rest and accelerates for 5s. He then travels at a constant velocity for 10s. Finally he slows down to a stop in 5s. Draw a distance time graph to represent his motion.
A sprinter starts from rest and accelerates for 5s. He then travels at a constant velocity for 10s. Finally he slows down to a stop in 5s. Draw a d-t graph to represent his motion. Then draw the corresponding v-t and a-t graphs
To draw a distance-time graph to represent the sprinter's motion, we can follow these steps:
1. Determine the time intervals and corresponding distances for each phase of the sprinter's motion: acceleration, constant velocity, and deceleration.
2. Assign time intervals and distances on the graph.
3. Plot the points and connect them with lines to represent the sprinter's motion.
Here's how it can be done:
1. For the acceleration phase of 5s, assuming constant acceleration, we can use the formula:
distance = initial velocity × time + (1/2) × acceleration × time²
Since the sprinter starts from rest, the initial velocity is 0. The acceleration is not mentioned, so let's assume it to be a constant value.
2. For the constant velocity phase of 10s, the sprinter travels the same distance with no change in time. So, the distance remains constant.
3. For the deceleration phase of 5s, again assuming constant deceleration, we can use the same formula as in the acceleration phase, but with a negative acceleration value since the sprinter is slowing down.
Once you have the distances calculated for each time interval, you can plot them on the graph. Time goes on the x-axis, and distance goes on the y-axis.
The graph will have three segments: a rising diagonal line for acceleration, a horizontal line for constant velocity, and a declining diagonal line for deceleration.