Question

an object accelerates at a rate of 1.2 m/s² w for 2.0 s and has an initial velocity of 5.0 m/s e. what is its final velocity? (a) 1.4 m/s e (b) 2.6 m/s e (c) 6.2 m/s w (d) 7.4 m/s w question 5 (1 point) which of the following describes a vector quantity? (a) an apple falls 6 m. (b) a fish swims at 1 m/s. (c) a student solves a puzzle in 10 min. (d) a car drives 60 km north

Explanation:

Step1: Define the variables

Let the east - west direction be along the \(x\) - axis. Let the east direction be positive (\(+x\)) and the west direction be negative (\(-x\)).
The initial velocity \(v_{0}=5.0\ m/s\) (east, so \(v_{0}= + 5.0\ m/s\)), the acceleration \(a=- 1.2\ m/s^{2}\) (west), and the time \(t = 2.0\ s\).
We use the kinematic equation \(v=v_{0}+at\).

Step2: Substitute the values into the equation

Substitute \(v_{0}=5.0\ m/s\), \(a=-1.2\ m/s^{2}\), and \(t = 2.0\ s\) into the equation \(v=v_{0}+at\).

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Since \(v = 2.6\ m/s>0\), the direction is east.

A vector quantity has both magnitude and direction.

• Option (a): "An apple falls 6 m" only gives magnitude (distance), no direction. It is a scalar.
• Option (b): "A fish swims at 1 m/s" only gives speed (magnitude), no direction. It is a scalar.
• Option (c): "A student solves a puzzle in 10 min" gives time (a scalar quantity).
• Option (d): "A car drives 60 km north" gives both magnitude (60 km) and direction (north). It is a vector.

Answer:

B. \(2.6\ m/s\ [E]\)