You are standing at the side of a road when you notice a car approaching. You me

Question

You are standing at the side of a road when you notice a car approaching. You measure its initial velocity vi and its constant acceleration a. Having studied 1-D motion with constant acceleration, you write down the following equations to describe the linear displacement %u0394s and change in velocity %u0394v of the car:

Explanation / Answer

1) a) distance travelled s = t*avarage lelocity............. s = t*(V+u)/2 = t*(U+at+u)/2 = u*t + (1/2)*a*t^2............. b) a = dv/dt ==> dv = a*dt............ c) workdone = change in KE............ m*a*s= (1/2)*m*(v2^2 - v1^2)............. m* a *s = (1/2)*m*(v2^2 - v1^2)................ v2^2 - v1^2 = 2*a*s.............. 2) a) angular displacement, theta = t*avarage angular vlelocity............. theta = t*(w1+w2)/2 = t*(w1+alfa*t +w1)/2 = w1*t + (1/2)*alfa*t^2............. b) alfa = dw/dt ==> dw = alfa*dt.............. c) workdone = change in KE............... Torque*theta = (1/2)*I*(w2^2 - w1^2).............. I*alfa*theta = (1/2)*I*(w2^2 - w1^2)............ w2^2 - w1^2 = 2*alfa*theta.................. w2^2 = w1^2 + 2*alfa*theta).................

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