Velocity and acceleration

Q.1 Two runners, Ayesha and fatima are leading the field in a long-distance race. They are both running at 5m/s with ayesha 10m behind fatima. when fatima is 50m from the tape, ayesha accelerates but fatima doesn't. what is the least acceleration ayesha must produce to overtake fatima ?
If instead fatima accelerates at 0.1 m/s2 up to the tape, what is the least acceleration ayesha must produce ?

2. A man is running for a bus at 3m/s. when he is 100m from the bus stop, the bus passes him going at 8m/s. Id deceleration of the bus is constant, at what constant rate should the man accelerate so as to arrive at the bus stop at the same instant as the bus?

Reply 1

e-n-i-g-m-a

OP

no need to answer question2 ..ive managed to do it ....but plz help me with question 1. !!!

Reply 2

yusufu

16

e-n-i-g-m-a

Q.1 Two runners, Ayesha and fatima are leading the field in a long-distance race. They are both running at 5m/s with ayesha 10m behind fatima. when fatima is 50m from the tape, ayesha accelerates but fatima doesn't. what is the least acceleration ayesha must produce to overtake fatima ?
If instead fatima accelerates at 0.1 m/s2 up to the tape, what is the least acceleration ayesha must produce ?

Ayesha has to run 60m in the same time as Fatima runs 50m.
for Fatima t = 50/5 = 10s
for Ayesha:
s=60 u = 5 t = 10 a = a
s = ut + ½at²
60 = 50 + 50a
minimum acceration = 0.2ms^-2

2. A man is running for a bus at 3m/s. when he is 100m from the bus stop, the bus passes him going at 8m/s. Id deceleration of the bus is constant, at what constant rate should the man accelerate so as to arrive at the bus stop at the same instant as the bus?

bus: s=100 u=8 v=0 t=t
t = 100/4 = 25s

man: s=100 u=3 t=25 a=a
s = ut+½at²
100 = 75 + ½(625)a
a = 0.08ms^-2

Velocity and acceleration

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