Question

The displacement of a body is represented as
x = 3t^4+4t^3+ t^2. Find its velocity and acceleration at the time, t = 2 s.

class 11 basic mathematics ​

Answer 1

s = 3t⁴ + 4t³ + t²

Differentiate both sides w.r.t t

==> ds/dt = 3dt⁴/dt + 4dt³/dt + dt²/dt

==> v = 12t³ + 12t² + 2t ...(1)

We need to find velocity at t = 2, So put t = 2 in (1)

==> v = 12(2)³ + 12(2)² + 2(2)

==> v = 12×8 + 12×4 + 4

==> v = 96 + 48 + 4

==> v = 148 units/s

Also,

Differentiate (1) w.r.t t

==> dv/dt = 12dt³/dt + 12dt²/dt + 2dt/dt

==> a = 36t² + 24t + 2 ...(2)

We need to find acceleration at t = 2 , so put t = 2 in (2)

==> a = 36(2)² + 24(2) + 2

==> a = 144 + 48 + 2

==> a = 194 units/s²