(3) The distance of a particle from a point O at time t seconds is given by s = 2t³ - 27t² + 108t - 84 metres for t≥ 0. (a) Find the velocity at time t. (b) Find the acceleration at time t. (c) Find the time(s) when the particle has a velocity of zero.

The bartender is totally amazing (must have studied physics). She slides your beer with an initial velocity of vo= 11.188 feet/second and the beer comes to a stop exactly in front of you after having slid a distance of d = 120.079 inches! Convert the sliding distance into proper units. d = meters meters/second Convert the initial velocity into proper units. Vo = Determine the acceleration of the beer as it slid down the counter (enter a negative number). a = Determine the time required for the beer to slide down the bar. t = seconds NOTE: The following may be helpful. . 1 foot 12 inches . 1 inch = 2.54 cm m/s²

العنوان оне hot small copper ball [c in kJ/kg.°C, k in W/m.°C] is suddenly placed in water maintained at 100 °C. The convection heat transfer coefficient is h in W/m². ºC. Derive equation to calculate the time required to reduce ball to temperature T.

) An object is thrown upward at time t = 0. After t seconds, its height is y = −4.9t² + 2t + 4.5 meters above the ground. (a) From what height was the object thrown? (b) What is the initial velocity of the object? (c) What is the acceleration due to gravity? meters m/s m/s²

A particle P projected from a point O on horizontal ground hits the ground after 2.4 seconds. The horizontal component of the initial velocity Of P is ms¯l. (a) Find, in termsofd, the horizontal distance ofPfrom O when it hits the ground. (b) Find the vertical commM1ent of the initial velocity of P. P just clears a vertical wall which is situated at a horizontal distance dm from O. (c) Find the height of the wall. The speed of pas it passes over the wall is 16m (d) Find the value Of d correct to 3 significant figures, o_2kg

The position at time t is greater than or equal to 0 of a particle moving along a coordinate line is given by s(t)=t^3+(3/2)t^2-6t a) Calculate the velocity and acceleration at time t b) Find the acceleration at each time the velocity is 0 c) When is the particle moving forward? When is it moving backwards?

Let  s(t)=2t^3- 21t^2 +72t in meters be the position of a particle moving on the coordinate line after t seconds on the interval [0, 6]. a. Find the instantaneous velocity at t = 2 seconds. b. Find the acceleration at t = 5 seconds. c.When is the particle moving in a positive direction? d. When is the particle moving in a negative direction? e. When is the particle at rest? Does s(0)-s(0) represent the total distance traveled from t = 0 to t = 6 seconds? Why or Why not?