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A particle moves in a straight line with...

A particle moves in a straight line with constant speed of `4 m//s` for `2 s,` then with `6 m//s` for `3 s.` Find the average speed of the particle in the given time interval.

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To find the average speed of the particle over the given time interval, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Given Data:** - Speed during the first interval (v1) = 4 m/s - Time for the first interval (t1) = 2 s - Speed during the second interval (v2) = 6 m/s - Time for the second interval (t2) = 3 s 2. **Calculate the Distance for Each Interval:** - Distance during the first interval (d1) can be calculated using the formula: \[ d1 = v1 \times t1 = 4 \, \text{m/s} \times 2 \, \text{s} = 8 \, \text{m} \] - Distance during the second interval (d2) can be calculated similarly: \[ d2 = v2 \times t2 = 6 \, \text{m/s} \times 3 \, \text{s} = 18 \, \text{m} \] 3. **Calculate the Total Distance:** - Total distance (D) is the sum of d1 and d2: \[ D = d1 + d2 = 8 \, \text{m} + 18 \, \text{m} = 26 \, \text{m} \] 4. **Calculate the Total Time:** - Total time (T) is the sum of t1 and t2: \[ T = t1 + t2 = 2 \, \text{s} + 3 \, \text{s} = 5 \, \text{s} \] 5. **Calculate the Average Speed:** - Average speed (V_avg) can be calculated using the formula: \[ V_{avg} = \frac{D}{T} = \frac{26 \, \text{m}}{5 \, \text{s}} = 5.2 \, \text{m/s} \] ### Final Answer: The average speed of the particle in the given time interval is **5.2 m/s**. ---

To find the average speed of the particle over the given time interval, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Given Data:** - Speed during the first interval (v1) = 4 m/s - Time for the first interval (t1) = 2 s - Speed during the second interval (v2) = 6 m/s ...
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Knowledge Check

  • A particle is moving on a straight line with constant retardation of 1 m//s^(2) . Its initial velocity is 10 m//s .

    A
    The distance travelled by the particle till it comes to rest is 50 m.
    B
    The average velocity till it comes to rest is `5 m//s`.
    C
    It comes to rest in 5 sec.
    D
    Its velocity after 5 sec is `5 m//s`
  • A particle is moving in a straight line under constant acceleration of 4 m//s^(2) . If its velocity at t=0 is 10 m//s, the displacement of particle in the 5^(th) second of its motion is

    A
    `28 m`
    B
    `100 m`
    C
    `34 m`
    D
    `50 m`
  • A particle moving in a straight line covers half the distance with speed of 3 m//s . The other half of the distance is covered in two equal time intervals with speed of 4.5 m//s and 7.5 m//s respectively. The average speed of the particle during this motion is :

    A
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    B
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    C
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