Question

A body travels in a straight line according to the equation, with its position given by the equation $x=4+3t-t^2$
The ratio of the distance travelled to the displacement covered in between $t=0$ to $t=2sec$ is :

• A. $\frac{8}{4}$
• B. $\frac{5}{4}$
• C. $1$
• D. $\frac{13}{6}$

Answer 1

The correct option is B $\frac{5}{4}$

Given $x=4+3t-t^2$,

Velocity $v=\frac{dx}{dt}=3-2t$,

Plotting the graph v-t as shown in the figure.

Area of velocity-time diagram gives the displacement.

Displacement $=\frac{1}{2}\times 3\times 1.5-\frac{1}{2}\times 1\times \frac{1}{2}=2$

Distance $=\frac{1}{2}\times 3\times 1.5+\frac{1}{2}\times 1\times \frac{1}{2}=\frac{10}{4}$

Ratio of distance to displacement$=\frac{\frac{10}{4}}{2}=\frac{5}{4}or5:4$