If a body travels a distance of d1, with a speed v1
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time taken is
t1=d1/v1
t1=d1/v1
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Let distance travelled with speed v1 be D1.
Let distance travelled with speed v2 be D2.
Time taken in both cases = t.
So we have :
Average speed = [math]total distance / total time taken[/math] = [math](D1+D2)/2t[/math]
[math]= (v1t+v2t)/2t = (v1+v2)/2.[/math]
But when times are different, we have :
Avg speed = [math]([/math][math]v1t1+v2t2)/(t1+t2)[/math]
Let distance travelled with speed v2 be D2.
Time taken in both cases = t.
So we have :
Average speed = [math]total distance / total time taken[/math] = [math](D1+D2)/2t[/math]
[math]= (v1t+v2t)/2t = (v1+v2)/2.[/math]
But when times are different, we have :
Avg speed = [math]([/math][math]v1t1+v2t2)/(t1+t2)[/math]
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