1. The graph represents the motion of an object.
- (a) The slope of the line is 5 m/s², which represents acceleration.
- (b) The area under the line from t=0 to t=4 s is 40 m, which represents displacement.
2. A ball is thrown upward with an initial velocity of 20 m/s.
- (a) Time to reach maximum height: t = v₀/g = 20/10 = 2 s
- (b) Maximum height: h = v₀²/(2g) = 400/20 = 20 m
3. A car accelerates uniformly from rest to 30 m/s in 6 seconds.
- (a) Acceleration: a = Δv/Δt = 30/6 = 5 m/s²
- (b) Distance traveled: d = ½at² = ½ × 5 × 36 = 90 m
4. An object falls freely from a height of 80 m.
- (a) Time to hit the ground: t = √(2h/g) = √(160/10) = 4 s
- (b) Velocity upon impact: v = gt = 10 × 4 = 40 m/s
5. A force of 20 N acts on a 5 kg mass.
- (a) Acceleration: a = F/m = 20/5 = 4 m/s²
- (b) If the force is doubled, acceleration becomes 8 m/s².
6. A 10 kg object is lifted vertically at constant speed.
- (a) Force required: F = mg = 10 × 10 = 100 N
- (b) Work done lifting 2 m: W = Fd = 100 × 2 = 200 J
7. A spring with k = 200 N/m is stretched 0.1 m.
- (a) Restoring force: F = kx = 200 × 0.1 = 20 N
- (b) Potential energy stored: PE = ½kx² = ½ × 200 × 0.01 = 1 J
8. A wave has frequency 50 Hz and wavelength 2 m.
- (a) Wave speed: v = fλ = 50 × 2 = 100 m/s
- (b) Period: T = 1/f = 1/50 = 0.02 s
9. A resistor of 10 Ω has a current of 2 A.
- (a) Voltage across it: V = IR = 2 × 10 = 20 V
- (b) Power dissipated: P = I²R = 4 × 10 = 40 W
10. A lens has focal length 15 cm. An object is placed 30 cm away.
- (a) Image distance: 1/f = 1/do + 1/di → 1/15 = 1/30 + 1/di → di = 30 cm
- (b) Magnification: m = -di/do = -30/30 = -1 (inverted, same size)
Parent Tip: Review the logic above to help your child master the concept of slope as rate of change worksheet.
