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Question :

To find the average speed of the bus during the following intervals

a) 10:30am to 11:30am

b) 11:30am to 1:30pm

c) 10:30am to 1:30pm

If the bus passed the 100km,160-km and 220-km points at 10:30am , 13:30 am and 1:30pm while travelling from Vijayawada to Hyderabad

Class : 11

Chapter : Motion in a straight line

Topic : Speed

Solution :

a) The distance covered between 10:30 a.m. to 11:30a.m. = 160km - 100km = 60 km

The time interval = 11:30 - 10:30 = 1 hour

The average speed during this interval = v₁ = 60km/1h = 60km/h

b) The distance covered between 11:30 a.m. to 1:30p.m. = 220km - 160km = 60 km

The time interval = 1:30 - 11:30 = 2 hour

The average speed during this interval = v₂ = 60km/2h = 30km/h

c) The distance covered between 10:30 a.m. to 11:30a.m. = 220km - 100km = 120 km

The time interval = 1:30 - 10:30 = 3 hour

The average speed during this interval = v₃ = 120km/3h = 40km/h

Answer :

• The average speed in 1st case is 60km/h

• The average speed in 2nd case is 30km/h

• The average speed in 3rd case is 40km/h

Know More :

Speed : It is the distance covered by a body in unit time time is called speed.

[tex]\mathrm{Speed} = \frac{distance}{time}\Rightarrow v=\frac{s}{t}[/tex]

There are different types of speeds to understand the motion of the bodies.

Average Speed : The average speed of a particle in a time interval is defined as the total distance travelled by the particle divided by the total time interval. If the particle travels a distance s in time t₁ to t₂, the average speed is defined as

[tex]\mathrm{v_a_v}=\frac{total\:\:distance}{total\:\:time}=\frac{s}{t_2-t_1}[/tex]

Instantaneous Speed : Let Δs be the distance travelled in the time to t + Δt. The average speed in the time interval is [tex]\mathrm{v_a_v}=\frac{\Delta s}{\Delta t}[/tex]

Now make Δt vanishingly small and look for the value of [tex]\frac{\Delta s}{\Delta t}[/tex]. Remember Δs is the distance travelled in the chosen time interval Δt. As Δt approaches 0, the distance Δs also approaches 0 but the ratio  [tex]\frac{\Delta s}{\Delta t}[/tex] has a finite limit.

The instantaneous speed at a time t is defined as [tex]v = \lim_{\Delta t \to \ 0} \frac{\Delta s}{\Delta t}=\frac{ds}{dt}[/tex] where s is the distance travelled in time t. The average speed is defined for a time interval and the instantaneous speed is defined at a particular instant. The dimensional formula of speed is LT⁻¹ and its SI unit is metre/second abbreviated as m/s

Uniform Speed : If an object travels equal distances in equal time intervals, it is said to move with uniform speed or constant speed. If an object moves with a uniform speed, its speed at any instant is the same as its average speed in that time interval. If it covers a distance S in a time interval t, its speed at any instant is given by the equation [tex]v=\frac{S}{t}\:\:or\:\:S=vt[/tex]

Non Uniform Speed : If an object travels equal distances in unequal time intervals, it is said to move with uniform speed.

Happy Learning!

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Explanation:

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