Effect of Mass and Force on Acceleration and Distance Traveled in Kinematics

[Karajovic]

[Solved] Kinematics ratio problem

Homework Statement

A force F produces an acceleration a when applied to a certain body. If the mass of the body is doubled and the force increased five-fold, what will be the effect on the following?
a. its acceleration

b. the distance the body travels in a given time

Homework Equations

The Attempt at a Solution

a. i know its acceleration is increased by 2.5 because if we have xa = 5f/2m, x=5/2

b. i know the distance is increased by 2.5, because everything else remains unchanged... but i can't seem to explain it in using equations... d = v1*t + 1/2at^2, if everything remains unchanged except a, we get: xd = 1/2(5/2a)1t^2 (assuming your velocity is 0 m/s?) i get that x = 5/4 but i know that's wrong, the distance can't be increased by 5/4...

 

[danago]

Homework Statement

A force F produces an acceleration a when applied to a certain body. If the mass of the body is doubled and the force increased five-fold, what will be the effect on the following?
a. its acceleration

b. the distance the body travels in a given time

Homework Equations

The Attempt at a Solution

a. i know its acceleration is increased by 2.5 because if we have xa = 5f/2m, x=5/2

b. i know the distance is increased by 2.5, because everything else remains unchanged... but i can't seem to explain it in using equations... d = v1*t + 1/2at^2, if everything remains unchanged except a, we get: xd = 1/2(5/2a)1t^2 (assuming your velocity is 0 m/s?) i get that x = 5/4 but i know that's wrong, the distance can't be increased by 5/4...

Remember that the 1/2 factor is there regardless if the acceleration is changed or not.

d₁ = 0.5at²
d₂ = 0.5(2.5a)t² = 2.5(0.5at²) = 2.5d₁

 

[Karajovic]

Remember that the 1/2 factor is there regardless if the acceleration is changed or not.

d₁ = 0.5at²
d₂ = 0.5(2.5a)t² = 2.5(0.5at²) = 2.5d₁

Thank you very much!