Question

Luigi is driving a steady 30 m/s when he passes Chiara, who is sitting in her car at rest. Chiarra, offended at his driving, begins to accelerate at a steady 2.0 m/s2 at the instant Luigi passes her.

How far does Chiara drive before passing Luigi?

How long does is take her to catch up to him?

What is her speed as she passes him?

When will she be 100 m ahead of him?

Answer 1

for Luigi

initial speed vL1 = 30 m/s

acceleration aL = 0

for Chiarra

initial speed vc1 = 0

acceleration ac = 2 m/s^2

at time t Chiarra drive pass LUigi

distance travelled by Luigi

XL = VL1*t = 30*t

distance travelled by Chiara

Xc = Vc1*t + (1/2)*aL*t^2 = (1/2)*2*t^2

XL = Xc

30*t = (1/2)*2*t^2

t = 30 s

distance travelled by Chiara XL = (1/2)*2*30^2 = 900 m   <<<<-------------ANSWER

-----------------------------------------

time taken to catch up to him , t = 30 s <<<<-------------ANSWER

----------------------------------------

v2L = v1L + aL*t

v2L = 0 + 2*30 = 60 m/s <<<<-------------ANSWER

--------------------------------------------

for Xc - XL = 100

v1L*t + (1/2)*aL*t^2 - VC1*t = 100

(1/2)*2*t^2 - 30*t = 100

time t = 33 s

at time 33 s she be 100 m ahead of him <<<<-------------ANSWER