Physics Speed and velocity help

Question

A student is walking with a constant speed of v1 m/s along High Street and sees a puddle d1 meters ahead of her. A bus driver is driving parallel to the student along High street/ The bus is d2 meters behind the student.The driver decides he wants to splash the student as she walks past. Determine the expression for the speed that the bus must have in terms of the given variables such that the bus and student reach puddle at the same time to splash student.

Answer 1

Hi Arika H.,

Distance divided by speed equals time. If I want to travel 20 meters with a speed of 10 meters per second it will take me 2 seconds, (20 m / 10 m/s = 2 s).

Let t_sp equal the students time to the puddle, t_bp equal the buses time to the puddle, and v₂ equal the speed of the bus.

d₁ / v₁ = t_sp, is the time it takes the student to get to the puddle.

(d₁ + d₂) / v₂ = t_bp, is the time it take the bus to reach the puddle. (d₁ + d₂ buses distance to the puddle).

We want the students time to the puddle and the buses time to the puddle to be equal. Lets set them equal to each other, t_sp = t_bp.

d₁ / v₁ = (d₁ + d₂) / v₂, but we need to solve for v₂ the speed the bus.

v₂ = v₁ * (d₁ + d₂) / d₁, this is your answer.

To check your work, pick some arbitrary numbers for d₁, d₂, and v₁, find v₂ then see if the times to the puddle are equal.

I hope this helps, Joe.

Answer 2

Student's speed : 1 m/s

1m/s

Bus__________2d__________Student_____d_____Puddle

It means after d second Student will arrive Puddle. (Time = Distance/Speed)

If Bus driver is using constant speed, he needs to travel 3d in d second, which means the speed is 3m/s.

If Bus driver is constantly accelerating from still (0 m/s) (Distance=1/2 at²)

3d = 1/2 a d²

a = 6/d m/s²