2. The position of a particle as a function of time is given by r() = (9.Oti +8.

Question

2. The position of a particle as a function of time is given by r() = (9.Oti +8.85j– 1.00tk)m, where [t]=s and [r]=m. Determine a) the particle's velocity and acceleration as a function of time. b) What are magnitudes of velocity and acceleration vectors at 2.50 s? 3. A skier is accelerating down (Fig. 1) a 30.0° hill at 1.80 m/sº. a) What is the vertical component of her acceleration? b) How long will it take her to reach the bottom of the hill assuming she starts from rest and accelerates uniformly, if the elevation change is 325 m? 4. A car is travelling on a road, slowing down to round the curve. Assume the curve has a shape of arc of a circle with radius 68 m. The driver has put the brakes on and the tangential acceleration at certain moment is 1.5 m/s. At the same time the instantaneous velocity of a car is 85 km/h. Calculate the magnitude and direction of the acceleration vector.

Explanation / Answer

here,

2)

r(t) = 9 i t + 8.85 j - 1 t^2 k

a)

differentiating the equation for v

v(t) = 9 i - 2 t k m/s .....(1)

differentiating equation (1) for a

a(t) = - 2 k m/s^2

b)

at t = 2.5 s

v(2.5) = 9i - 2 * 2.5 k m/s

magnitude , |v| = sqrt(9^2 + 5^2) = 10.3 m/s

at t = 2.5 s

a(2.5) = - 2 k m/s^2

|a| = 2 m/s^2

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