Question

A body travels at 12 m/s for 10 minutes and at
20 m/s for the next to 20 minutes. Find its
Average speed​

Answer 1

Given :

A body travels at 12m/s for 10min and at 20m/s for the next 20min.

To Find :

Average speed of body.

Solution :

❒ Average speed of body is defined as the ratio of total distance travelled to the total time taken.

• It is a scalar quantity having only magnitude.
• It can't be negative or zero.
• SI unit : m/s

First of all we need to convert unit of time from min to second.

We know that, 1 min = 60 s

» t₁ = 10 min = 10 × 60 = 600 s

» t₂ = 20 min = 20 × 60 = 1200 s

$\sf:\implies\:v_{av}=\dfrac{d_1+d_2}{t_1+t_2}$

We know that distance is measured as the product of velocity and time. [d = v t]

$\sf:\implies\:v_{av}=\dfrac{v_1t_1+v_2t_2}{t_1+t_2}$

$\sf:\implies\:v_{av}=\dfrac{(12)(600)+(20)(1200)}{600+1200}$

$\sf:\implies\:v_{av}=\dfrac{7200+24000}{1800}$

$\sf:\implies\:v_{av}=\dfrac{31200}{1800}$

$:\implies\:\underline{\boxed{\bf{\orange{v_{av}=17.33\:ms^{-1}}}}}$

Answer 2

Answer:

Question

A body travels at 12 m/s for 10 minutes and at

20 m/s for the next to 20 minutes. Find its

Average speed

GIVEN

• Speed 1 =12m /sec
• time 1 = 10 min
• speed 2 = 20 m/sec
• time 2 = 20 min

To find

Average speed

Solution

❁Average speed is defined as the ratio between the total distance and total time .

$\boxed { \sf \purple{Average \: speed = \frac{ D_{1} + D_{2}}{t_{1} + t_{2}} }}$

Distance is defined as :-

$\boxed{ \sf{ \to \: Distance \: = speed \times time}}$

Now convert the time from minutes to seconds :

1 minute = 60 seconds

By using unitary method

→ 10 minutes= 600 seconds.

→ 20 minutes= 1200 seconds.

Now substitute the values of average speed in the formula of " average speed".

$\sf{ \to average \: speed = \frac{12 \times 600+ 20 \times 120 0}{600 + 1200} } \\ \\ \sf{ \to average \: speed = \frac{7200 + 24000}{1800} } \\ \\ \sf{ \to average \: speed = \frac{31200}{1800 } } \\ \\ \sf \blue{ \to average \: speed =17.3 \: m \: {sec}^{ - 1} }$

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More information!!

✏️Scalar quantities are only expressed as magnitude. E.g: time, distance, mass, temperature, area, volume

✏️Vector quantities are expressed in magnitude as well as the direction of the object. E.g: Velocity, displacement, weight, momentum, force, acceleration, etc.

✏️Speed is the rate of change of distance. If a body covers a certain distance in a certain amount of time

✏️The Rate of change of displacement is velocity. It is a vector quantity.

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