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- A linear approximation is an approximation of a general function using a linear function.
- The linear equation formula is given as
y = f(a) + f'(a)(x-a)
where, f(a) is the function of curve.
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- A high-tech drone flies over Miami, FL in a direction 50.4 west of north with a speed of 35.4 km/h. Three hours later, the drone suddenly shifts due north, and its speed slows to 19.2 km/h. How far (in kilometers) from Miami, FL is the drone 4.50 h after it passes over the Miami. Round your answer to 0 decimal places.A kangaroo can jump over an object 1.3 m high. Considering just its vertical motion, how long the kangaroo is in the air (hint: consider up and down motions)? Write the answer in seconds. of on Answer: 0.515A car travels 64.70 +/- 0.50 meters in 8.650+/-0.05 seconds. What is its speed in m/s? Answer must have correct number of significant digits .Do not have the include the error in the answer.
- A car starts from 2.0 m/s and accelerates at 4.0 m/s for 6.0 s, it then coasts for 5.0 s. How far has it traveled, in meters? Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometersper hour (km/h) and (b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)A bird flies 3.50 km [East] and then immediately turns around and flies 7.50 km [West]. The bird's average speed for the entire motion is 11.0 km/h. What is the bird's average velocity. Give your answer in km/h to 2 decimal places. A velocity that is west should be treated as negative and a negative sign should be included in your answer. A velocity that is east should be treated as positive but no sign should be included in the answer. Do not include units in your answer.
- 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.An adventure racer ran 1.7 km north, then 3.2 km 63° to the south of due east, then 1.4 km west. She completed the trip in 2 hr: 5 min :8 s. What was the magnitude of her average velocity over the entire trip in m/s? Express your answer in metres/second to two decimal places (do not include units in your answer).A person drops a rock from the edge of a cliff that is 1350 ft high. The initial acceleration is a=−32 ft/sec^2. 1. What is the velocity equation? Use t as the variable and v for the velocity. 2. What is the displacement equation? Use t as the variable and s as the displacement. 3.What time did it hit the ground? (Hint: s=0) 4. What was the velocity just before impact?
- A car starts from 2.0 m/s and accelerates at 4.0 m/s2 for 6.0 s. How far has it traveled, in meters? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.QUESTION 3 Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. Pedro is driving a motorcycle along Espana boulevard. His position x (in meters) at any given time t is given by x(t) = 1.124t2 + 6.022. Pedro's initial position is X = m. His position at ten seconds is X = m. His speed at ten seconds is V= m/s. His acceleration at ten seconds is a = m/s2. Marites is also driving her motorcycle along Espana. Her position function is of the form x(t) = Ct. what is the coefficient C if her acceleration at ten seconds is 2.04 m/s2? C= m/s4A pumpkin is shot straight up with an initial speed of 5.9 m/s. What is the maximum height it can reach, in meters? Use g = 10 m/s2.Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.