Suppose you have a 2 kg toy car that can move along a flat road in the x-directi

Question

Suppose you have a 2 kg toy car that can move along a flat road in the x-direction. You can ignore friction. This car has a cheap little engine in it that takes a while to get going... so the force it puts on the car is a function of time: (t) = 5t (with the appropriate SI units implied). If the car's initial velocity is 8 m/s (say you gave it a push beforehand) and its initial position is zero, find the car's velocity and position after 3 seconds. Answer: 19.25 m/s, 35.25 m Taylor, Chapter 1, #41 Answer: Tension = mR Omega 2, radially inward Taylor, Chapter 1, #29

Explanation / Answer

the force applied on car instantanously=5*t x^ So the acceleration on the car= 2.5*t and acceleration= d^2x/dt^2=2.5*t ===>dx/dt=(2.5/2)*t^2+c1 ==>x= (2.5/6)*t^3+c1*t+c2 But the conditions given were at x=0,at t=0===>c2=0 and dx/dt=8 at t=0===> c1=8 and x=(2.5/6)*t^3+8*t dx/dt=(2.5/2)*t^2+8 then at t=3 ,subsitute in above equation,we get the answers

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