Question

A particle moving in a straight line covers half the distance with speed 4 m/s. The other half of the distance is covered in two equal time intervals with speed 5 ms- and 7 m/s respectively. The average speed of the particle during this motion is​

Answer 1

Answer:

periodic Motion

Explanation:

Answer 2

Given data : A particle moving in a straight line covers half the distance with speed 4 m/s. The other half of the distance is covered in two equal time intervals with speed 5 m/s and 7 m/s respectively.

To find : The average speed of the particle during this motion ?

Solution : Let, total distance covered by partical be x.

Now, a/c to given data;

• Speed of the particle = 4 m/s
• Distance covered by the partical = x/2
• Time taken by partical, T[1] = ?

By formula of speed;

➜ speed = distance/time

➜ 4 = (x/2)/T[1]

➜ T[1] = x/(2 *4)

➜ T[1] = x/8 ----{1}

similarly {The other half of the distance is covered in two equal time intervals with speed 5 m/s and 7 m/s respectively}

Hence,

➜ x/2 = T[2] * 5 + T[3] * 7

Where, T[2] and T[3] are time intervals.

A/C to given data; T[2] = T[3]

Hence,

➜ x/2 = T[2] * 5 + T[2] * 7

➜ x/2 = 12 * T[2]

➜ T[2] = x/(2 * 12)

➜ T[2] = x/24

Hence, T[2] = x/24 and T[3] = x/24

Now,

➜ Total time taken = T[1] + T[2] + T[3]

➜ Total time taken = x/8 + x/24 + x/24

➜ Total time taken = 3x/24 + x/24 + x/24

➜ Total time taken = (3x + x + x)/24

➜ Total time taken = 5x/24

Now,

➜ Average speed = Total distance/total time taken

➜ Average speed = x/(5x/24)

➜ Average speed = 24x/5x

➜ Average speed = 4.8 m/s

Answer : The average speed of the particle during this motion is is 4.8 m/s.

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