Question

The velocity-displacement graph for a car on a straight road is shown in figure


Determine the acceleration of the car at $s=150\text{m}$.

• A. $62.5{\text{m/s}}^2$
• B. $114{\text{m/s}}^2$
• C. $15.625{\text{m/s}}^2$
• D. $10.75{\text{m/s}}^2$

Answer 1

The correct option is C $15.625{\text{m/s}}^2$

Referring to the $v-s$ graph,
Slope of graph for $100\text{m}<s<200\text{m}$
$\text{Slope}=\frac{dv}{ds}=\frac{75-50}{200-100}=\frac{25}{100}=\frac{1}{4}$
Equation of the above part of graph is
$(v-50)=\frac{1}{4}(s-100)$

Let $v_1$ be velocity when $s=150\text{m}$
Then, $v_1-50=\frac{1}{4}[150-100]$
$v_1=50/4+50=62.5\text{m/s}$
So, acceleration when $s=150\text{m}$ will be
$a=\frac{dv}{dt}=v\frac{dv}{ds}=62.5\times \frac{1}{4}$
$a=15.625{\text{m/s}}^2$