Question

Q1.A particle moves along the x-axis. The function v(t) gives the particle's velocity at any time t≥0:
v(t)=t2−8t+16
What is the particle's velocity v(t) and acceleration a(t) at t=3?

Answer 1

Answer:

given v(t) = t²-8t+16

v(t) directly gives the velocity at any particular time and derivative of v(t) gives the acceleration.

acceleration a = dv/dt = 2t - 8

velocity at t = 3 is,

v = (3)² -8(3) +16

v= 9 - 24 + 16

v = 1 m/sec

now acceleration at t = 3 sec is

a = 2(3) - 8

a = 6 - 8

a = -2 m/sec² ( deceleration )