Question

Starting from rest a car moves with an acceleration for sometime. Then it moves with uniform velocity for<br />a while and finally retards with the same rate and comes to rest. If the total distance covered the body and the total<br />time taken be S and t respectively, then show that the car was in uniform velocity for a time<br />$\sqrt{t {}^{2} - \frac{4s}{a} }$<br />​

Answer 1

Answer:

Explanation:

Avg speed × total times = total distance

20×25=500

Since acceleration in the 1st interval is same as deceleration in the 3rd interval and deceleration is from the same velocity achieved after acceleration, t  

1

​  

=t  

3

​  

 

s  

1

​  

=  

2

1

​  

×5t  

1

2

​  

 

s  

2

​  

=(5t  

1

​  

)t  

2

​  

 

s  

3

​  

=(5t  

1

​  

)×t  

3

​  

−  

2

1

​  

×5×t  

1

2

​  

=(5t  

1

​  

)×t  

1

​  

−  

2

1

​  

×5×t  

1

2

​  

 

s  

1

​  

+s  

2

​  

+s  

3

​  

=5t  

1

​  

t  

2

​  

+5t  

1

2

​  

 

⇒5t  

1

2

​  

+5t  

1

​  

t  

2

​  

=500−−−−1

2t  

1

​  

+t  

2

​  

=25−−−−2

Solving (1 ) and   (2) ⇒t  

1

​  

=5,t  

2

​  

=15sec