Question

The velocity displacement curve for an object moving along a straight line is shown in the given figure. At which of the marked points, the object is speeding up?

• A. 1
• B. 2
• C. 1 and 3
• D. 1, 2 and 3

Answer 1

The correct option is A 1

We know that if acceleration and velocity are in same direction then the speed of the body increases.
Acceleration of the body is given by
$a=V\frac{dV}{ds}$
We can find the sign of acceleration at various points, $V$ is +ve, for all three points 1, 2 and 3.
$\frac{dV}{ds}$ is +ve for point 1, zero for point 2 and –ve for point 3.
So, only for point 1, velocity and acceleration have same sign. So, the object is speeding up at point 1 only. Hence, the correct answer is option (a).