it is denoted by

s = ut + ½ at 2

Distance=Initial Velocity × Time + 1/2acceleration × time 2


s = Distance Travelled

u = Initial Velocity

t = time taken

a = acceleration


How is this Equation Derived?





Q 1 Page 109 - A bus starting from rest moves with a uniform acceleration of 0.1 m s-2 for 2 minutes. Find (a) the speed acquired, (b) the distance travelled

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Q 4 Page 110 - A racing car has a uniform acceleration of 4 m s-2. What distance will it cover in 10 s after start?

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NCERT Question 4 - A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m s–2 for 8.0 s. How far does the boat travel during this time?

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Example 8.6 - A car accelerates uniformly from 18 km h–1 to 36 km h – 1 in 5 s.Calculate (i) the acceleration and (ii) the distance covered by the car in that time.

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Example 8.7 - The brakes applied to a car produce an acceleration of 6 m s-2 in the opposite direction to the motion. If the car takes 2 s to stop after the application of brakes, calculate the distance it travels during this time.

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  1. Class 9
  2. Chapter 8 Class 9 - Motion


Second Equation of Motion - Derivation s = ut + 1/2 π‘Žπ‘‘^2 Derivation πœ‹Γ— We know that Velocity = π·π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘/π‘‡π‘–π‘šπ‘’ Velocity Γ— Time = Displacement Displacement = Velocity Γ— Time If Velocity is not constant (i.e. Velocity keeps on increasing or decreasing) We can also take Average Velocity in place of Velocity So our formula becomes Displacement = Average Velocity Γ— Time Displacement = (πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™ π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦ + πΉπ‘–π‘›π‘Žπ‘™ π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦)/2 Γ— Time s = ((𝑒 + 𝑣)/2) Γ— t From first equation of motion, we know that: v = u + at Putting value of v in this equation s = ((𝑒 + (𝒖 + 𝒂𝒕))/2) Γ— t s = ((2𝑒 + π‘Žπ‘‘)/2) Γ— t s = (2𝑒/2+π‘Žπ‘‘/2) Γ— t s = (𝑒+1/2 π‘Žπ‘‘) Γ— t s = 𝑒𝑑+1/2 π‘Žπ‘‘^2

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CA Maninder Singh is a Chartered Accountant for the past 9 years and a teacher from the past 16 years. He teaches Spoken English, Written English, Grammar and Vocabulary at Englishtan.