Number 1: Three blocks (block P, block q, and block R) are all initially at rest. Block P is the most massive, and block R is the least massive. Identical horizontal forces push each block, causing them to accelerate, for five seconds. Assuming the coefficient of friction between the block and the surface is the same in all cases, which block will have the highest amount of kinetic energy?

1
a) Block Q

b) Block P

c) Block R

d) They all have the same kinetic energy, although they have different speeds

well, KE = 1/2 * m * (v squared)

as you know v = a * t

thus KE = 1/2 * m * (a squared) * (t squared)

rearrange the above equation you get (assuming m * a = F)

KE = 1/2 * F * a * (t squared)

since the question stated the horizontal force and time of acceleration are same for all three blocks, so it really depends on acceleration

F = m * a (force is still same for three objects)

inversely proportional relationship between m and a.

Thus, R is the answer

I'm not 100% sure about my answer, so ask physics TA at your school.

Number 2: A spring-loaded dart gun is used to shoot a dart straight up into the air. The same dart is shot up a second time from the same gun, but this time the spring is compressed twice as far in comparison to the first shot. How far up does the dart go this time? Neglect friction and assume the spring obey's hooke's law.

a) Half the dist

b) twice the dist

c) four times the dist

d) eight times the dist

1/2 * k * (x squared) = m g h

k, g, and m will be same for both conditions

x -> 2x

1/2 * k * ((2x) squared) = m * g * h

1/2 * k * (4 (x squared)) = m * g * 4h

c is the answer

hope this helps

good luck

Thanks a bunch