Question

The velocity-time graph shows the motion of a cyclist. Find (i) its acceleration ii) its velocity and (iii) the distance covered by the cyclist in 15 seconds.

Velocity (m s) 5 10 15 20 25 Time (S) —> 

Answer 1

Step1: Given a graph

Step2: Formula Used

1. Acceleration: The rate of change of velocity with respect to time is known as acceleration. $a=\frac{dv}{dt}$ where a, v and t are acceleration, velocity, and time respectively.
2. Velocity: The definition of velocity for an object is the rate at which the object's position changes in relation to a frame of reference and time. $v=\frac{dx}{dt}$where v,x, and t are velocity, displacement, and time respectively.
3. $Dis\tan ce\left(s\right)=velocity\left(v\right)\times time\left(t\right)$

Step3: Calculating acceleration

The acceleration is $0m/s^2$ since the velocity is constant.

Step4: Calculating Velocity

From the graph, we can infer that the velocity is constant and it is $20m/s$

Step5: Calculating the Distance covered by the cyclist in 15 seconds

The Distance covered by the cyclist in 15 seconds = During that time period, the area under the v-t graph

$$\begin{gathered} s=vxt \\ s=20x15 \\ s=300m \end{gathered}$$

Hence (1) accleration is

(2) velocity is

(3) distance covered in 15 seconds =$300m$