A car is made to accelerate along a ramp path, inclined at 30^o with the horizontal,at a=3t³+t m/s. Determine its velocity and position at t = 4s given t = 0, s = 0.
1) 200 m/s & 164.266 m
2) 300 m/s & 164.266 m
3) 250 m/s & 300 m
4) 210 m/s & 430 m

Velocity:
Since a = f(t),the car's position can be determined from a = d²s/dt². Note that,s = 0 at t = 0.
Integrating the acceleration function we find velocity and position-

Thus the velocity of the car at t = 4s is
Hence at t = 4s, the velocity of the car is 200 m/s and the distance travelled by car is 164.27 m.

Position