You are in your car and pushing the gas pedal so that your acceleration is const

Question

You are in your car and pushing the gas pedal so that your acceleration is constant. If you travel 250 m between the time when your speedometer reads 40km/h and 60 km/h how long did it take you to travel that 250 m? What was your acceleration during that time? You throw a ball straight up and measure that it reaches height h and stays in the air for time t. If you want the ball to stay in the air for time 2t, to what maximum height should you throw it? Your initial velocity will be the same for both throws.

Explanation / Answer

4)
given

v1 = 40 km/h = 40*5/18 m/s = 11.1 m/s

v2 = 60 km/h = 60*5/18 m/s = 16.7 m/s

d = 250 m

let a is the acceleration of the car and t is the time taken.

use, v2^2 - v1^2 = 2*a*d

==> a = (v2^2 - v1^2)/(2*d)

= (16.7^2 - 11.1^2)/(2*250)

= 0.31 m/s^2

now use, v2 = v1 + a*t

==> t = (v2 - v1)/a

= (16.7 - 11.1)/0.31

= 18.1 s

5) h = v^2/(2*g)

v = sqrt(2*g*h)

and

time of flight,

t = 2*v/g

in the second case

time of flight, 2*t = 2*v'/g

2*2*v/g = 2*v'/g

2*v = v'

v' = 2*sqrt(2*g*h)

maximum height reached by the object,
H = v'^2/(2*g)

= (2*sqrt(2*g*h))^2/(2*g)

= 4*h <<<<<<-----------Answer

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