Haruki's 4 kg cart is already rolling at 3 m/s when a 20 N net force starts acting forward on it. The force acts for 2 s.
How fast is the cart moving when the force stops?
A chain of short steps carries you from force and time to the final velocity.
Take the cart's direction of travel as positive.
Step 1: find the impulse. J = FΔt.
Step 2: the theorem turns the impulse into the momentum change. Δp = J.
Step 3: divide by the mass to get the velocity change. Δv = Δp/m.
Step 4: add the change to the starting velocity. v_final = v_initial + Δv.
A backward force makes the impulse negative, so the chain subtracts instead of adds.
A 4 kg cart rolls at 3 m/s. A 20 N net force acts forward on it for 2 s. Calculate its final velocity.
Write down the values:
m = 4 kg, v_initial = 3 m/s, F = 20 N, Δt = 2 s, v_final = ?
Find the impulse:
J = 20 × 2 = 40 (N·s)
The momentum change equals it: Δp = 40 kg·m/s
Find the velocity change:
Δv = 40/4 = 10 (m/s)
Add it to the start:
v_final = 3 + 10 = 13
The cart leaves at 13 m/s.
The same 4 kg cart, later, moves at 9 m/s when a 10 N net force acts backward on it for 2 s. Take its direction of travel as positive. Calculate its final velocity.
Write down the values:
m = 4 kg, v_initial = 9 m/s, F = −10 N (backward), Δt = 2 s, v_final = ?
Find the impulse:
J = −10 × 2 = −20 (N·s)
The momentum change equals it: Δp = −20 kg·m/s
Find the velocity change:
Δv = −20/4 = −5 (m/s)
Add it to the start:
v_final = 9 − 5 = 4
The cart slows to 4 m/s.
A 5 kg sled on smooth snow moves at 6 m/s. A 30 N net force acts forward on it for 1.4 s. Enter the impulse delivered in N·s.
The same 5 kg sled takes that impulse. Using your impulse answer, enter the sled's gain in velocity in m/s.
The sled started at 6 m/s. Enter its final velocity in m/s.
A 7 kg wagon moves at 3 m/s. A 14 N net force acts forward on it for 4 s. Enter its final velocity in m/s.
Take the cart's direction of travel as positive. A 40 kg cart coasts at 9 m/s; a 120 N net force acts backward on it for 2.5 s. Enter its final velocity in m/s.
Take the crate's direction of travel as positive. A 10 kg crate slides at 2.4 m/s when a 40 N net force starts acting backward on it, lasting 1.25 s. Enter its final velocity in m/s (keep the sign).