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A Car Starts from rest and travelled 100m in the first 10s. Assuming uniform acceleration, Calculate the distance it will travel in the next 10s.

Physics

ScanSolve AI Answer

Answer

300 m300 \, \text{m}

Step-by-step solution

3 steps
  1. Calculate the acceleration of the car.

    The car starts from rest, so its initial velocity u=0 m/su = 0 \, \text{m/s}.
    It travels a distance s1=100 ms_1 = 100 \, \text{m} in time t1=10 st_1 = 10 \, \text{s}.
    Using the kinematic equation s=ut+12at2s = ut + \frac{1}{2}at^2:

    100=(0)(10)+12a(10)2100 = (0)(10) + \frac{1}{2}a(10)^2 100=0+12a(100)100 = 0 + \frac{1}{2}a(100) 100=50a100 = 50a a=10050a = \frac{100}{50} a=2 m/s2a = 2 \, \text{m/s}^2
  2. Calculate the total distance traveled in the first 20 s20 \, \text{s}.

    The car travels for the first 10 s10 \, \text{s} and then for the next 10 s10 \, \text{s}, making a total time t2=10 s+10 s=20 st_2 = 10 \, \text{s} + 10 \, \text{s} = 20 \, \text{s}.
    Using the same initial velocity u=0 m/su = 0 \, \text{m/s} and the calculated acceleration a=2 m/s2a = 2 \, \text{m/s}^2:

    s2=ut2+12at22s_2 = ut_2 + \frac{1}{2}at_2^2 s2=(0)(20)+12(2)(20)2s_2 = (0)(20) + \frac{1}{2}(2)(20)^2 s2=0+1(400)s_2 = 0 + 1(400) s2=400 ms_2 = 400 \, \text{m}
  3. Calculate the distance traveled in the next 10 s10 \, \text{s}.

    This is the difference between the total distance traveled in 20 s20 \, \text{s} and the distance traveled in the first 10 s10 \, \text{s}.
    Distance in next 10 s=s2−s110 \, \text{s} = s_2 - s_1
    Distance in next 10 s=400 m−100 m10 \, \text{s} = 400 \, \text{m} - 100 \, \text{m}
    Distance in next 10 s=300 m10 \, \text{s} = 300 \, \text{m}

    The distance the car will travel in the next 10 s10 \, \text{s} is 300 m\boxed{300 \, \text{m}}.

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