At t=0 , a body starts from origin with some initial velocity. the displacement x in m of the body varies with time in s as x= -2/3t sqr + 16t +2. find the initial velocity of the body and also find how long does the body come to rest. what is the acceleration of the body when it come to rest.
Answers
Answered by
1
Velocity = Δ in Displacement with time
Acceleration = Δ in velocity with time
Since in this case we are given a displacement function, we get the velocity and acceleration by differentiating x with respect to time.
For velocity we take the first derivative.
For acceleration we take the second derivative.
Velocity
Dx/dt of x = - 2/3t² + 16t + 2
V = - 4/3t + 16
Acceleration
= d²x/dt²
= - 4/3
Initial velocity
At the start point t = 0
Initial velocity = - 4/3 × 0 + 16
= 16m/s
The time taken by the body to come to rest.
At rest the velocity = 0
Hence :
-4/3t + 16 = 0
-4/3t = - 16
-4t = - 48
t = 48/4
t = 12 seconds
Acceleration = - 4/3 m/s²
The negative sign indicates that the body is decelerating.
Similar questions