Net displacement for a particle in motion with velocity function
v(t)= -3t + 8m/sec from time t =0 to t = 4 is equal to 8units.
As given in the question,
Velocity function of the particle is given by :
v(t)= -3t + 8 m/sec
Particle is in motion from time t = 0 to t =4
Let us consider 's' be the net displacement of the particle
Initial velocity by v(0) at t = 0 is
v(0) = -3(0) + 8
= 8m/sec
Final velocity by v(4) at t= 4
v(4) = -3(4) + 8
= -4m/sec
Total time 't' = 4 - 0
= 4 units
Net displacement :
s = ( 1/2) ( v(4) + v(0) ) t
⇒ s = (1/2)( -4 + 8)(4)
⇒ s = (1/2)(4)(4)
⇒ s = 8 units
Therefore, for the given velocity function and time the net displacement is equal 8 units.
The complete question is :
Determine the net displacement of a particle in motion from t=0 to t=4 given that the velocity function for the particle is v(t)=−3t+8 m/sec. Do not include any units in your answer.
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