A bicyclist in the Tour de France has a speed of 32.0 miles per hour (mi/h) on a flat section of the road. What is this speed in (a) kilometers per hour (km/h), and (b) meters per second (m/s)? (a) Number i (b) Number i Units Units

An object is dropped from rest and takes 2.42 seconds to reach the ground below. From what distance above the ground was it dropped? State this as a positive number and assume it has proper SI Units.

The velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.

d²y Let 4 - 5y = 0, suppose the solution has the form y = e1x. - dx2 dx Find the Characteristic Equation of å and find the roots of the equation.

The acceleration of an object (in m/s) is given by the function a(t) = 7 sin(t). The initial velocity of the object is v(0) 2 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. meters

The following times are given using metric prefixes on the base SI unit of time: the second. Rewrite them in scientific notation without the prefix (in s). For example, 47 Ts would be rewritten as 4.7 ✕ 1013 s. (Enter your answers as m ✕ 10n, where 1 ≤ |m| < 10  and n is an integer.) 984 Ps 986 fs 19 ns 572 µs

(a) Suppose that the displacement x of an object is related to time t according to the expression x = Bt2. What are the dimensions of B? T O T/L O L/L O UT O LT? OLXT2 Use L to stand for the dimension of length, and T to stand for the dimension of time, What is the dimension of x? of t? Can you solve the equation for B? (b) Suppose the displacement x of another object is related to time t according to x = A sin(2ft), where A and fare constants. What are the dimensions of A? (Hint:A trigonometric function appearing in an equation must be dimensionless.) O T/L O LUT OL OL x T OT

Consider the physical quantities s, v, a, m, and t with dimensions [s] = L, [v] = LT-¹, [a] = LT-2, [m] = M, and [t] = T. Select the dimensionally consistent equation(s). U √2as = v S = vtm + a = U S = at at² m

Bicyclists in the Tour de France reach speeds of 500 miles per hour (mi/h) on flat sections of the road. What is this speed in kilometers per second (km/sec)? cf. 1 mile = 1.609 km

Sweet corn plants can grow 4.1 cm in heightper day. What is this speed in (a) millimeters per second and(b) feet per week?