Can anyone PLEASE help me with these word problems?!?

Question

pls. show and explain how you did it.

1)what velocity is attained by an object that is accelerated at 0.40 m/s squared for displacement of 64 m if its initial velocity is 2 m/s?

2)Arnel is to design a runway for planes whose take off velocity is 60 m/s and can accelerate constantly at 12 m/s squared.how long should be the runway?

3)a car which is moving in a straight line steadily increases its speed from 50 kph to 60 kph in 30 mins. what is the acceleration of the car?

4)a racing car starting from rest accelerates at a rate of 5 m/s. what is the velocity of the car after it has traveled 100m?

Answer 1

1. the equations of motion or this type of 1-d uniform acceleration are:

x(t) = x_o + v_o(t) + (1/2)a(t^2)

v(t) = v_o + at

with x_o = 0, v_o = 2 m/s, a_o = .4 m/s^2

v(t) = 2 + .4t

x(t) = x_o + 2t + .2t^2 = 2t + .2t^2

Now we find t for x = 64

64 = 2t + .2t^2 (multiply by 10)

640 = 20t + 2t^2

-2t^2 - 20t + 640 = 0

Using the quadratic formula the solutions are: t = 13.574, and t = -23.574 So t = 13.574 is the only solution with physical meaning.

Putting t = 13.574 into the velocity equation will give it velocity when x = 64

v(13.574) = 2 + .4(13.574)

= 7.4296 m/s

that's your answer.

Attempt the other ones or try another poster.

bye for now.

Answer 2

1) use the equation

v(final)^2 = v(initial)^2 + 2 a d  where a is accel and d is distance traveled

in this case, you want to solve for v(final) setting v(initial)=2, a=0.4 and d =64

2)  use the same equation, but here solving for d; in this case v(initial)=0, v(final)=60m/s and a = 12 m/s/s

3) this is a direct use of the definition of acceleration, which is change in velocity divided by time

the change in velocity is 10 km/hr and the time in which the change occurs is 1/2 hour (be careful to use consistent units), so the acceleration is 10km/h / 0.5 hr = 20 km/hr/hr

4)  use the equation I gave you in no. 1; v(initial)=0, a=5m/s/s and d=100 m, solve for v(final).  (This is an easy one:

vf^2 = 0+2x5x100 or vf=sqrt(1000)