Question

If V – T graph of a motion is straight line inclined to the axes, then choose all correct statements

Velocity is constant

a is constant

displacement is proportional to square of the time

v ∝ t

Answer 1

1. False. Since the line is not parallel to T-axis, the velocity is not constant.

2. True. By definition, the acceleraton is the slope of the V(T) graph. For the straight line the slope is the same for each T (constant).

3. False. The equation of the velocity as the straight line is: $V(T) = kT + b$ where $k,b$ are some constants. By definition, the distlacement is given as follows: $d(T) = \int V(T)dt = \int (kT + b) dT = \dfrac{kT^2}{2} + bT + c$, where $c$ is some constant of integration. As one can see, $d(T)$ is not directly proportinal to the T in general (but this can be true when $b = c = 0$).

4. False. Again, since $V(T) = kT + b$, V(T) is not proportional to T in general. But this can be true when $b = 0$.