A toy car has an initial speed of 2 m/s at t = 0, and accelerates at a = 0.1 v 2

Question

A toy car has an initial speed of 2 m/s at t = 0, and accelerates at a = 0.1v2 m/s2 for 3 seconds. The brakes are then applied and the car has a constant deceleration of 4 m/s2 until it comes to rest.

(a) Determine the total time of travel.

A toy car has an inital speed of 2 ms at A toy car has an initial speed of 2 m/s at t = 0 and accelerates at a = 0.1 v2 m/s2 for 3 seconds. The brakes are then applied and the car has a constant deceleration of 4 m/s2 until it comes to rest. (a) Determine the total time of travel. (b) Determine the total distance traveled.

Explanation / Answer

for first 3 seconds,the accelaration a = 0.1*v^2

A) at the end of first 3 seconds,the sfinal speed is V1

then v1 = 2+ integral (a*dt) = 2+ integral (0.1*v^2*dt) = 2+(0.1*v^3/3) limits from 0 to 3

V1 = 2+ (0.1*3^3/3) = 2+ (0.9) = 2.9 m/s

the time taken for deccelaration is t2

t2 = (v2-v1)/(-a) = (0-2.9)/(-4) = 0.725 S

total time taken is 3+0.725 = 3.725 S

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B) total distance travelled is S1+S2

accelaration = a = 0.9/3 = 0.3 m/s^2

S1 = (2*3) + (0.5*0.3*3*3) = 7.35 m

S2= (2.9*0.725)-(0.5*4*0.725*0.725) = 1.05 m

ten total distance travelled is S1+S2 = 7.35+1.05= 8.4 m

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