Problem 1: A car starts at rest and moves along a perfectly straight highway wit

Question

Problem 1: A car starts at rest and moves along a perfectly straight highway with an acceleratiorn of al = 10 m/s2 for a certain amount of time tl. It then moves with constant speed (zero acceleration) for a time t2 and finally decelerates with an acceleration a2-10 m/s2 for a time t3 until it comes to a complete stop. The total time of motion is t1 t2 t3 25 s. The total distance travelled by the car is 1 km. Find t2. Hints: (i) Recognize that each segment of the journey is at constant acceleration! (ii) What is the relationship between the quantities t1, t2, and t3? Use this to help simplify the set of equations that you obtain during the solution process.

Explanation / Answer

t1+t2+t3=25

distance travelled in time t1=0.5*10*t12=5t12

velocity after time t1=10t1

distance travelled in time t2=10t1*t2

duration of deceleration=t3

magnitude of deceleration=10 m/s2

10t1/t3 = 10

or, t1=t3

distance trevelled in time t3 = 10t1*t3+(0.5*-10*t32)=10t1t3-5t32

but t1=t3

distance travelled in t3=10t12-5t12=5t12

total distnace travelled = 5t12+10t1t2+5t12 = 10t12+10t1t2 = 1000

Or, t12+t1t2 = 100...(i)

also, t1+t2+t3=25

Or, 2t1+t2=25...(ii)

t2=25-2t1

t12+t1(25-2t1)=100

Or, t12-25t1+100=0

t1=5 seconds

t2 = 25-(2*5)=15 seconds

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