Question

The distance travelled by a particle moving along a straight line is given by x = 180t + 50t². Find initial velocity, velocity at t = 4s and acceleration.​

Answer 1

Distance (Displacement)

x = 180t+50t²

We know Differentiation of displacement gives instantaneous velocity,

So,

v = dx/dt = d180t+50t²/dt = 180+100t

Now,

Initial velocity, that is t= 0

v = 180+100t= 180+100×0 = 180m/s

Initial velocity = 180m/s

Velocity at t=4s

v = 180+100t = 180+100×4 = 180+400 = 580m/s

We know, Differentiation of velocity gives acceleration,

so,

a = dv/dt = d180+100t/dt = 100

So Acceleration = 100m/s²

Cheers!