Homework SourseThe acceleration function in m s 2 and the initial velocit
The acceleration function ( in m / s 2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.
a(t)=t+2,v(0)=5,0<=t<=10
a(t)=t+2,v(0)=5,0<=t<=10
Solution
v(t) = Integral of (a(t)) = t^2/2 +2t + c
V(0) = 5, therefore c = 5
v(t) = (t^2)/2 + 2t +5
distance = Integral (0 to 10) v(t) = (10^3 -0 )/ 6 + 10^2 - 0^2 +5*(10 -0) = 316.67
