Question

The displacement of the body x(in meters) varies with time t (in sec) asx=−23t2+16t+2x=−23t2+16t+2find followinga. what is the velocity at t=0,t=1b. what is the acceleration at t=0c. what is the displacement at t=0d. what will the displacement when it comes to reste. How much time it takes to come to rest.​

Answer 1

x = -23t²+16t+2

dx/dt = v = -46t+16

dv/dt = a = -46

a) Velocity at t = 0

v = -46t+16

For t = 0

v = 16 m/s

b) Velocity at t = 1

v = -46t+16

For t = 1

v = -30 m/s

c) Acceleration is constant = -46 m/s²

d) Displacement at t = 0

x = -23t²+16t+2

For t = 0

x = 2 m

e) Time taken to reach at rest

At rest, v = 0

v = -46t+16

0 = -46t+16

46t = 16

t = 16/46 = 8/23 = 0.34 seconds

f) Displacement when at rest

For rest, t = 8/23

x = -23t²+16t+2

x = -23 × 64/529 + 16 × 8/23 + 2

x = -1472/529 + 128/23 + 2

x = -2.7 + 2 + 2.41

x = 1.71 m