Question

1
A particle is moving in a straight line such that its
displacement (X) is related to time (t) as
X = (3 - 4t + 5t2)m. The correct velocity-time
(v-t) graph will be​

Answer 1

A particle is moving in a straight line such that its displacement (x), is related to time (t), as x = 3 - 4t + 5t²

we have to show velocity - time graph

you know as well, velocity is the rate of change of displacement with respect to time. i.e., v = dx/dt

so, differentiate given equation with respect to time,

dx/dt = d(3 - 4t + 5t²)/dt

or, v = 0 - 4 + 10t

or, v = 10t - 4 this is a straight line equation of slope 10 and velocity intercept is (-4).

A tough diagram of velocity - time graph is shown in figure.