two cars are racing on a linear track that has a lenght of 1500meters. Car (a) h

Question

two cars are racing on a linear track that has a lenght of 1500meters. Car (a) has an initial velocity of 10.0 m/s and accelerates at a rate of 1.00 m/^2.Car (b)starts with a velocity of 4.00 m/s and an acceleration of 2.00 m/s^2.

a)what is the distance travelled bu each car 10.0 seconds after the race begins?

b)what is the velocity of each car after 10.0 seconds?

c)what is the velocity of each car at the end of the race?

d)how long will it takefor each car to complete the race?

e)after how how many seconds will car (b) overtake car (a)?

Explanation / Answer

a.)

using equn of motion

distance travel by Car A

S = ut + 0.5at^2

S = 10*10 + 0.5*1*10^2 = 150 m

distance travel by Car B

S = ut + 0.5at^2

S = 4*10 + 0.5*2*10^2

S = 140 m

b.)

For Car A

V = u + at

V = 10+ 1*10

V = 20 m/s

For Car B

V = u + at

V = 4 + 2*10

V = 24 m/s

c.)

using equn of motion

For car A

V^2 = u^2 + 2as

V^2 = 10*^2 + 2*1*1500

v = 55.677 m/s

For Car B

V^2 = u^2 + 2as

V^2 = 4*^2 + 2*2*1500

v = 77.51 m/s

d.)

For Car A

V = u + at

55.677 = 10 + 1*t

t =45.677 sec

For Car B

V = u +at

77.51 = 4 + 2t

t = 36.75 sec

e.) using equn of motion

S1 = u1t + 0.5 a1t^2

S2 = u2t + 0.5 a2t^2

u2t + 0.5 a2t^2 = u1t + 0.5 a1t^2

4t + t^2 = 10t + 0.5t^2

t = 12 sec

at t=12 sec car b will overtake Car A

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