A car accelerates uniformly from rest to a speed of 25 m/s in 10 seconds.
(a) Calculate the acceleration of the car.
(b) Calculate the distance travelled during this time.
Given:
Initial velocity u=0 m/su = 0 \, m/su=0m/s
Final velocity v=25 m/sv = 25 \, m/sv=25m/s
Time t=10 st = 10 \, st=10s
(a) Acceleration
Formula: a=v−uta = \frac{v – u}{t}a=tv−u
a=25−010=2.5 m/s2a = \frac{25 – 0}{10} = 2.5 \, m/s^2a=1025−0=2.5m/s2
✔ Acceleration = 2.5 m/s²
(b) Distance traveled
Formula: s=ut+12at2s = ut + \frac{1}{2}at^2s=ut+21at2
s=0×10+12×2.5×102s = 0 \times 10 + \frac{1}{2} \times 2.5 \times 10^2s=0×10+21×2.5×102 s=12×2.5×100=125 ms = \frac{1}{2} \times 2.5 \times 100 = 125 \, ms=21×2.5×100=125m
✔ Distance = 125 m
A bulb has a resistance of 20 Ω and is connected across a 10 V battery.
Find the current flowing through the bulb.
Formula: I=VRI = \frac{V}{R}I=RV
I=1020=0.5 AI = \frac{10}{20} = 0.5 \, AI=2010=0.5A
✔ Current = 0.5 A
A student lifts a 5 kg bag vertically through 2 m.
Calculate the work done against gravity (Take g=9.8 m/s2g = 9.8 \, m/s^2g=9.8m/s2).
Formula: W=mghW = mghW=mgh
W=5×9.8×2=98 JW = 5 \times 9.8 \times 2 = 98 \, JW=5×9.8×2=98J
✔ Work done = 98 Joules
A wave has a frequency of 200 Hz and a wavelength of 1.5 m.
Calculate the wave speed.
Formula: v=fλv = f \lambdav=fλ
v=200×1.5=300 m/sv = 200 \times 1.5 = 300 \, m/sv=200×1.5=300m/s
✔ Wave Speed = 300 m/s
An object has a mass of 600 g and volume 250 cm³.
Calculate its density.
Convert mass to kg: 600g=0.6kg600 g = 0.6 kg600g=0.6kg
Convert volume to m³: 250cm3=2.5×10−4m3250 cm³ = 2.5 \times 10^{-4} m³250cm3=2.5×10−4m3
Formula: ρ=mV\rho = \frac{m}{V}ρ=Vm
ρ=0.62.5×10−4=2400 kg/m3\rho = \frac{0.6}{2.5 \times 10^{-4}} = 2400 \, kg/m^3ρ=2.5×10−40.6=2400kg/m3
✔ Density = 2400 kg/m³